Systems Seminar
Compressed Sensing and Blind Sensor Array Calibration
Rob Nowak
UW ECE Department
Abstract
In this talk I will discuss two non-traditional sampling problems. In
the first part of the talk, we will reconsider the way we sample and
acquire signals. Today, most signals are acquired by sensing and
sampling at a high rate (at least twice the bandwidth), as dictated by
the Shannon-Nyquist sampling law. However, once a signal is acquired,
compressing the sampled data is often the next step. Audio and speech
signals are acquired by acoustic sensors that are sampled in time at a
very high rate, and then later they are compressed into MP3 files.
Images and videos are densely sampled, and then compressed into JPEG
and MPEG files. If signals can be drastically compressed after
sensing and sampling, is it really necessary to sample at such a high
rate in the first place? The answer, which flies in the face of
conventional wisdom, is no. It is possible to reconstruct a signal
from a relatively small number of samples, a number proportional to
the number of bits required in the optimal compression of the signal.
Moreover, these key samples need not be adaptive, instead they take
the form of randomized projections of the signal. This idea, called
Compressed Sensing, is causing a dramatic re-thinking of the basic
fundamentals of sensing and sampling. This talk will describe the
basic theory and methods of CS, and discuss potential applications of
CS in medical imaging and wireless sensor networks.
In the second part of the talk I consider the problem of blindly
calibrating sensor networks using routine measurements. I will show
that as long as the sensors slightly oversample the signals of
interest, then unknown sensor gains can be perfectly
recovered. Remarkably, neither a controlled stimulus nor a dense
deployment is required. I will also characterize necessary and
sufficient conditions for the identification of unknown sensor
offsets. These results exploit incoherence conditions between the
basis for the signals and the canonical or natural basis for the
sensor measurements. Practical algorithms for gain and offset
identification based on the singular value decomposition will be
presented. The robustness of the proposed algorithms to model mismatch
and noise are investigated with both simulated data and using data
from current sensor network deployments.
Time and Place: Wed., Jan. 31, at 3:30 pm in 4610 Engr. Hall.
SYSTEMS SEMINAR WEB PAGE:
http://homepages.cae.wisc.edu/~gubner/seminar/schedule.html